A normal curve is a bell-shaped curve which shows the
probability distribution of a continuous random variable.The term
“bell curve” is usually used in the social sciences; in statistics,
it’s called a normal distribution.
The mean (average) is always in the center of a bell curve or
normal curve.
A bell curve / normal curve has only one mode, or peak. Mode
here means “peak”; a curve with one peak is unimodal; two peaks is
bimodal, and so on.
A bell curve / normal curve has predictable standard deviations
that follow the 68/ 95 /99.7 rule.A standard deviation is a unit of
measurement that can help you with figuring out where data items
are likely to fall. For example, 68% of all measurements fall
within one standard deviation either side of the mean. In other
words, the bulk of your data will fall between -1 and +1 standard
deviations from the mean. If you go out to two standard deviations,
that percentage rises to 95; almost all (99.7%) of your data will
fall within three standard deviations.
A bell curve / normal curve is symmetric. Exactly half of data
points are to the left of the mean and exactly half are to the
right of the mean.
The normal is also statistically convenient. It is represented
by two parameters which are arguably the most basic statistics
there are: the average and the variance (or standard deviation).
The average is the most basic statistic there is.
It is used to determine the percentage of cases in a normal
distribution within given limits.The Normal Probability Curve helps
us to determine:
i. What percent of cases fall between two scores of a
distribution.
ii. What percent of scores lie above a particular score of a
distribution.
iii. What percent of scores lie below a particular score of a
distribution.
It is used to compare two distributions in terms of-
overlapping:-If scores of two groups on a particular variable are
normally distributed. What we know about the group is the mean and
standard deviation of both the groups. And we want to know how much
the first group over-laps the second group or vice-versa at that
time we can determine this by using the table area under NPC.
NPC helps us in dividing a group into sub-groups according to
certain ability and assigning the grades:-When we want to divide a
large group in to certain sub-groups according to some specified
ability at that time we use the standard deviation units of a NPC
as units of scale.
NPC is useful to normalize a frequency distribution:-In order
to normalize a frequency distribution we use Normal Probability
Curve. For the process of standardizing a psychological test this
process is very much necessary.
To test the significance of observations of experiments we use
NPC:-In an experiment we test the relationship among variables
whether these are due to chance fluctuations or errors of sampling
procedure or it is real relationship. This is done with the help of
table area under NPC.
NPC is used to generalize about population from the sample:-We
compute standard error of mean, standard error of standard
deviation and other statistics to generalize about the population
from which the sample are drawn. For this computation we use the
table area under NPC.